Acrylated product, wherein it can be obtained by simultaneous or successive and alternating reactions between a) a polyol R(OH)m or a mixture of polyols R(OH)m, having a functionality m of at least 3 for a polyol a) alone, or having a number-average functionality with respect to m greater than 2.1 for a mixture of polyols R(OH)m and b) the acrylic acid (R1OH) in stoichiometric deficit relative to a), and in the presence of c) at least one cyclic carboxylic anhydride or of its polyacid form having a carboxy group functionality z ranging from 2 to 4, with an overall ratio r=CO2H/OH of less than 1 with r1 being the ratio of the carboxy groups of c) to the carboxy groups of b) acrylic acid, r1=(carboxy)c/(carboxy)b, wherein R is the residual radical of a polyol of valency m or a mixture of polyols of valency m and R1 is an acryloyl radical.